Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrodinger system

In this paper, we establish two new types of invariant sets for the coupled nonlinear Schrodinger system on $\mathbb{R}^n$, and derive two sharp thresholds of blow-up and global existence for its solution. Some analogous results for the nonlinear Schrodinger system posed on the hyperbolic space $\mathbb{H}^n$ and on the standard 2-sphere $\mathbb{S}^2$ are also presented. Our arguments and constructions are improvements of some previous works on this direction. At the end, we give some heuristic analysis about the strong instability of the solitary waves.Comment: 21 page

Dissecting early regulatory relationships in the lamprey neural crest gene network

The neural crest, a multipotent embryonic cell type, originates at the border between neural and nonneural ectoderm. After neural tube closure, these cells undergo an epithelial–mesenchymal transition, migrate to precise, often distant locations, and differentiate into diverse derivatives. Analyses of expression and function of signaling and transcription factors in higher vertebrates has led to the proposal that a neural crest gene regulatory network (NC-GRN) orchestrates neural crest formation. Here, we interrogate the NC-GRN in the lamprey, taking advantage of its slow development and basal phylogenetic position to resolve early inductive events, 1 regulatory step at the time. To establish regulatory relationships at the neural plate border, we assess relative expression of 6 neural crest network genes and effects of individually perturbing each on the remaining 5. The results refine an upstream portion of the NC-GRN and reveal unexpected order and linkages therein; e.g., lamprey AP-2 appears to function early as a neural plate border rather than a neural crest specifier and in a pathway linked to MsxA but independent of ZicA. These findings provide an ancestral framework for performing comparative tests in higher vertebrates in which network linkages may be more difficult to resolve because of their rapid development

Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems

A rigorous justification of several well-known mathematical models of incompressible fluid flows can be given in terms of singular limits of the scaled Navier-Stokes-Fourier system, where some of the characteristic numbers become small or large enough. We discuss the problem in the framework of global-in-time solutions for both the primitive and the target system. © 2010 Springer Basel AG

A Second-Generation Device for Automated Training and Quantitative Behavior Analyses of Molecularly-Tractable Model Organisms

A deep understanding of cognitive processes requires functional, quantitative analyses of the steps leading from genetics and the development of nervous system structure to behavior. Molecularly-tractable model systems such as Xenopus laevis and planaria offer an unprecedented opportunity to dissect the mechanisms determining the complex structure of the brain and CNS. A standardized platform that facilitated quantitative analysis of behavior would make a significant impact on evolutionary ethology, neuropharmacology, and cognitive science. While some animal tracking systems exist, the available systems do not allow automated training (feedback to individual subjects in real time, which is necessary for operant conditioning assays). The lack of standardization in the field, and the numerous technical challenges that face the development of a versatile system with the necessary capabilities, comprise a significant barrier keeping molecular developmental biology labs from integrating behavior analysis endpoints into their pharmacological and genetic perturbations. Here we report the development of a second-generation system that is a highly flexible, powerful machine vision and environmental control platform. In order to enable multidisciplinary studies aimed at understanding the roles of genes in brain function and behavior, and aid other laboratories that do not have the facilities to undergo complex engineering development, we describe the device and the problems that it overcomes. We also present sample data using frog tadpoles and flatworms to illustrate its use. Having solved significant engineering challenges in its construction, the resulting design is a relatively inexpensive instrument of wide relevance for several fields, and will accelerate interdisciplinary discovery in pharmacology, neurobiology, regenerative medicine, and cognitive science

An NF-κB and Slug Regulatory Loop Active in Early Vertebrate Mesoderm

BACKGROUND: In both Drosophila and the mouse, the zinc finger transcription factor Snail is required for mesoderm formation; its vertebrate paralog Slug (Snai2) appears to be required for neural crest formation in the chick and the clawed frog Xenopus laevis. Both Slug and Snail act to induce epithelial to mesenchymal transition (EMT) and to suppress apoptosis. METHODOLOGY & PRINCIPLE FINDINGS: Morpholino-based loss of function studies indicate that Slug is required for the normal expression of both mesodermal and neural crest markers in X. laevis. Both phenotypes are rescued by injection of RNA encoding the anti-apoptotic protein Bcl-xL; Bcl-xL's effects are dependent upon IκB kinase-mediated activation of the bipartite transcription factor NF-κB. NF-κB, in turn, directly up-regulates levels of Slug and Snail RNAs. Slug indirectly up-regulates levels of RNAs encoding the NF-κB subunit proteins RelA, Rel2, and Rel3, and directly down-regulates levels of the pro-apopotic Caspase-9 RNA. CONCLUSIONS/SIGNIFICANCE: These studies reveal a Slug/Snail–NF-κB regulatory circuit, analogous to that present in the early Drosophila embryo, active during mesodermal formation in Xenopus. This is a regulatory interaction of significance both in development and in the course of inflammatory and metastatic disease

Current perspectives of the signaling pathways directing neural crest induction

The neural crest is a migratory population of embryonic cells with a tremendous potential to differentiate and contribute to nearly every organ system in the adult body. Over the past two decades, an incredible amount of research has given us a reasonable understanding of how these cells are generated. Neural crest induction involves the combinatorial input of multiple signaling pathways and transcription factors, and is thought to occur in two phases from gastrulation to neurulation. In the first phase, FGF and Wnt signaling induce NC progenitors at the border of the neural plate, activating the expression of members of the Msx, Pax, and Zic families, among others. In the second phase, BMP, Wnt, and Notch signaling maintain these progenitors and bring about the expression of definitive NC markers including Snail2, FoxD3, and Sox9/10. In recent years, additional signaling molecules and modulators of these pathways have been uncovered, creating an increasingly complex regulatory network. In this work, we provide a comprehensive review of the major signaling pathways that participate in neural crest induction, with a focus on recent developments and current perspectives. We provide a simplified model of early neural crest development and stress similarities and differences between four major model organisms: Xenopus, chick, zebrafish, and mouse

Measurement of Z0 decays to hadrons, and a precise determination of the number of neutrino species

We have made a precise measurement of the cross section for e+e--->Z0-->hadrons with the L3 detector at LEP, covering the range from 88.28 to 95.04 GeV. From a fit to the Z0 mass, total width, and the hadronic cross section to be MZ0=91.160 +/- 0.024 (experiment) +/-0.030(LEP) GeV, [Gamma]Z0=2.539+/-0.054 GeV, and [sigma]h(MZ0)=29.5+/-0.7 nb. We also used the fit to the Z0 peak cross section and the width todetermine [Gamma]invisible=0.548+/-0.029 GeV, which corresponds to 3.29+/-0.17 species of light neutrinos. The possibility of four or more neutrino flavors is thus ruled out at the 4[sigma] confidence level.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28683/3/0000500.pd

A measurement of the Z0 leptonic partial widths and the vector and axial vector coupling constants

We have measured the partial widths of the Z0 into lepton pairs, and the forward-backward charge asymmetry for the process e+e--->[mu]+[mu]- using the L3 detector at LEP. We obtain an average [Gamma]ll of 83.0+/-2.1+/-1.1 MeV.From this result and the asymmetry measurement, we extract the values of the vector and axial vector couplings of the Z0 to leptons: grmv=-0.066-0.027+0.046 and grmA= -0.495-0.007+0.007.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28666/3/0000483.pd

Measurement of electroweak parameters from hadronic and leptonic decays of the Z 0

We have studied the reactions e + e − →hadrons, e + e − , μ + μ − and τ + τ − , in the energy range 88.2 GeV. A total luminosity of 5.5 pb −1 , corresponding to approximately 115000 hadronic and 10000 leptonic Z 0 decays, has been recorded with the L3 detector. From a simultaneous fit to all of our measured cross section data, we obtain assuming lepton universality:Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47890/1/10052_2005_Article_BF01475788.pd